n/(n+1)!=1/n!-1/(n+1)!,
（1/2的阶乘+2/3的阶乘+.+n/(n+1)的阶乘）=1/n!-1/(n+1)!+1/(n-1)!-1/n!+...
+1/2!-1/3!+1/1!-1/2!=1-1/(n+1)!
故（1/2的阶乘+2/3的阶乘+.+n/(n+1)的阶乘）的极限为1.